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\large{Name:} \hfill    \large{Probability for Scientists, Fall 2013}

\hfill    \large{ Bio 409 / Bio 509 / Stat 479 } 

\hfill    \large{ Quiz 11 (5 pts) }

\hfill    \large{ 22 Oct 2013 }

\section*{CGS Ch 7}
1. Inductive reasoning argues \uline{~~~~~~~~~~~~~} from a set of
\uline{~~~~~~~~~~~~~} to a reasonable hypothesis.
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2. An eccentric billionaire is obsessively interested in the mean weight of
North American pigeons.  This billionaire employs a loyal army of dedicated
field assistants to collect 1,000 random samples of said pigeons.  For each
sample, a sample mean $\hat{\mu}$ and 95\% confidence interval (CI) is produced.
How many of these 1,000 CI do you expect to contain the true population mean
$\mu$?
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3. A confidence interval is defined by $(1-\alpha)\%$, such that $\alpha=0.05
\iff 95\%$ CI.  For a given sample, how does the CI change as $\alpha$ gets
smaller (e.g. $\alpha$ goes from 0.05 to 0.01)?
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4. Let $\hat{p} = \frac{x}{N}$ represent the proportion of successes of a sample
of size N, where the true population proportion of successes equals p.  If one
were to draw many samples (to get many instances of $\hat{p}$), then the 
sampling standard deviation of $\hat{p} = \sigma(\hat{p}) = $
\uline{~~~~~~~~~~~~~}.
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As N gets larger, how does $\sigma(\hat{p})$ change? 

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